ECEN 5448/MCEN 5228: Advanced Linear Systems (Fall 2016-2021)
This graduate-level control course focusses on basic analysis of linear control systems using state-space approaches. Topics include internal stability, Lyapunov theory, controllability and observability, transfer functions and realizations, pole placement and feedback stabilization, calculus of variation, Pontryagin's maximum principle, linear quadratic regulators.
ECEN 5488: Geometric Control Theory (Fall 2022 and Spring 2017, 2020)
This graduate-level course introduces geometric approaches to investigate continuous-time control systems. Topics include manifolds and vector fields, Lie groups and Lie algebras, controllability and Lie algebra rank conditions, group actions and equivariant dynamics, perturbation theory, Lyapunov theory, Riemannian metrics and gradient flows, feedback stabilization, and ensemble control and estimation theory. Basic concepts from topology, differential geometry, and Lie groups/algebras will be introduced as needed.
ECEN 5498: Stochastic Control Theory (Fall 2020 and Spring 2019)
This graduate-level course develops tools for investigating continuous-time stochastic control systems. Continuous-time stochastic differential equation is a fundamental tool for modeling real-world phenomena, with major applications in physics, biology, finance, and engineering. A necessary step towards this goal is to introduce the basics of Ito calculus. We will do so in two steps: first, we will discuss Poisson jump processes. This class of processes can be used to model continuous-time Markov chain, among other things. We will spend some time exploring the subject and introduce the Ito rule, show how to derive the density equation (Fokker-Planck equation). In the second step, we will introduce Brownian processes as limits of jump processes, discuss system theoretic issues, and derive the (continuous-time) Kalman-Bucy filter.
ECEN 3810: Intro to Probability (Spring 2021, 2022 and Fall 2019)
This undergraduate-level course covers the fundamentals of probability theory. The goal of the course is to introduce basic concepts of random variables and a toolbox for analyzing their fundamental properties.